Skip to main content

Full text of "06. Measurement Uncertainty in NA - Part 3 v2"

See other formats


ISSN 2310-6697 

otoiser — open transactions on independent scientific-engineering research 



FUNKTECHNIKPLUS # JOURNAL 



Theorie — Experimentation — Metrologie — Logiciel — Applications 

ISSUE 2 - SUNDAY 17 NOVEMBER 2013 - YEAR 1 

REPRINT 



Measurement Uncertainty in Network Analyzers: 
Differential Error Analysis of Error Models 
Part 3: Short One-Port Calibration -Comparison 

N.I. Yannopoulou, P.E. Zimourtopoulos 




jssjHggsgr: 



About 



This small European Journal is 

In the Defense of Honesty in Science and Ethics in Engineering 

Publisher - otoiser — open transactions on independent scien- 
tific engineering research, www. otoiser . org - info§otoiser . org, 
HauptstraBe 52, 2831 Scheiblingkirchen, Austria 

Language - We declare the origins of the Journal by using 
in the cover page English, German and French, as well as, a 
Hellenic vignette. However, since we recognize the dominance 
of US English in the technical literature, we adopted it as the 
Journal's language, although it is not our native language. 

Focus - We consider Radio-FUNK, which still creates a vivid 
impression of the untouchable, and its Technology-TECHNIK, 
from an Advanced-PLUS point of view, Plus-PLUS Telecommunica- 
tions Engineering, Electrical Engineering and Computer Sci- 
ence, that is, we dynamically focus at any related scien- 
tific-engineering research regarding Theorie, Experimenta- 
tion, Metrologie, Logiciel, ou Applications. 

Scope - We emphasize this scope broadness by extending the 
title of the Journal with a Doppelkreuz-Zeichen # which we 
use as a placeholder for substitution of our Editorial Team 
disciplines: # Telecommunications etc. as above, or # High 
Voltage, # Software Engineering, # Simulation etc. as below. 

Frequency - We publish 3 issues per year: on 31st of Janu- 
ary, on 31st of May, and on 30th of September, as well as, an 
extra issue every 3 papers and a volume every 2 years. 

Editions - We increase the edition number of an issue only 
when is needed to reform one or more of its papers — thus to 
increase their version numbers — but we keep unchanged its 1st 
edition date shown on its front page and we number its pages 
sequentially from 1. We count the editions of About separately. 

Format - We use a fixed-space font, hyphenation, justifica- 
tion, unfixed word spacing, and the uncommon for Journals A5 
(half A4 ) page size to achieve WYSIWYG printing and clear 
reading of 2 to 4 side-by-side pages on wide-screen displays 

Printing-on-Demand - We can email gratis PDFs at 300-4000 
dpi in booklet page scaling of either brochure or book type. 

Copyright - We publish under a Creative Commons Attribution, 
CC-BY 3.0 Unported or CC-BY 4.0 International, License only. 

Please download the latest About edition from 

about . f tp j . otoiser . org 



FUNKTECHNIKPLUS # JOURNAL 



e3—2 



ISSUE 7 - YEAR 2 



About 



About 



Editorial Team 

# Electrical Engineering 

# High Voltage Engineering # Insulating Materials 
Professor Michael Danikas, mdanikas@ee.duth.gr 
EECE, Democritus University of Thrace, Greece 

# Electrical Machines # Renewable Energies # Electric Vehicles 
Assistant Professor Athanasios Karlis, akarlis@ee.duth.gr 
EECE, Democritus University of Thrace, Greece 

# Computer Science 

# Computer Engineering # Software Engineering # Cyber Security 
Professor Vasilis Katos, vkatos@bournemouth.ac.uk 

Head of Computer and Informatics Dept, Bournemouth Univ, UK 

# Internet Engineering # Learning Management Systems 
Lecturer Sotirios Kontogiannis, skontog@gmail.com 
Business Administration Dept, TEI, Western Macedonia, Greece 

# Hypercomputation # Fuzzy Computation # Digital Typography 
Dr. Apostolos Syropoulos, asyropoulos@yahoo.com 
BSc-Physics, MSc-Computer Science, PhD-Computer Science 
Independent Researcher, Xanthi, Greece 

# Telecommunications Engineering 

# Applied EM Electromagnetics # Applied Mathematics 
Dr. Nikolaos Berketis, nberketis@gmail.com 
BSc-Mathematics, MSc-Applied Maths, PhD-Applied Mathematics 
Independent Researcher, Athens, Greece 

# Antennas# Metrology# EM Software # Simulation# Virtual Labs 

# Applied EM # Education # FLOSS # Amateur Radio # Electronics 
Dr. Nikolitsa Yannopoulou, yin@arg . op4 . eu * 

Diploma Eng-EE, MEng-Telecom-EECE, PhD-Eng-Antennas-EECE 
Independent Researcher, Scheiblingkirchen, Austria 
Dr. Petros Zimourtopoulos, pez@arg . op4 . eu * 

BSc-Physics, MSc-Radio-Electronics, PhD-Antennas-EE 
Independent Researcher, Scheiblingkirchen, Austria 

# Copy & Layout Editing - Proof Reading - Issue & Web Management 

Technical Support 

Konstantinos Kondylis, kkondylis@gmail.com 
Diploma Eng-EECE, MEng-EECE, Doha, Qatar 

Christos Koutsos, ckoutsos@gmail.com 

Diploma Eng-EECE, MEng-EECE, Bratislava, Slovakia 



Information for Authors 

This is a small, but independent, low profile Journal, in 
which we are all — Authors, Reviewers, Readers, and Editors — 
free at last to be Peers in Knowledge, without suffering from 
Journal roles or positions, Professional-Amateur-Academic sta- 
tuses, or established "impact factorizations", under the fol- 
lowing guiding principles: 

Authors - We know what Work means, we respect the Work of 
the Independent Researcher in Science and Engineering and we 
want to exhibit his Work. Thus, we decided to found this Free 
and Open Access Journal in which to publish this Work. Fur- 
thermore, as we care indeed for the Work of the technical au- 
thor — especially a young or a beginner one — we strongly sup- 
port the publication of his Work, as follows: 

Q We do not demand from the author to transfer his own copy- 
right to us. Instead, we only consider papers resulting from 
original research work only, and only if the author can as- 
sure us that he owns the copyright of his own paper as well 
as that he submits to the Journal either an original copy or 
a revised version of his own paper, for possible publica- 
tion after review — or even for immediate republication, if 
this paper has already been published after review — but, in 
any case under a Creative Commons Attribution, CC-BY 3 Un- 
ported or CC-BY 4 International, License, only. 

1 We encourage the author to submit his own paper written 
just in Basic English plus Technical Terminology. 

2 We encourage the author even to select a pen name, which 
may drop it at any time to reveal his identity. 

3 We encourage the author to submit an accepted for publica- 
tion paper, which he was forced to decline that publicati- 
on because it would be based on a review with unacceptable 
evaluation or derogatory comments. 

4 We encourage the author to submit any paper that was rejected 
after a poor, impotent, inadequate, unreasonable, irrespon- 
sible, incompetent, or "just ticking" review. 

5 We encourage the author to submit an unreviewed paper of his 
own that he uploaded on some Open Access repository. 

6 We encourage the author to upload his published papers in 
our Journal to a truly Free Open repository like vixra.org. 

7 We provide the author with a decent, express, peer review 
process, of up to just 4 weeks, by at least 2, either 
anonymous or onymous, reviewers. 



SUNDAY 31 MAY 2015 e3-3 FUNKTECHNIKPLUS # JOURNAL FUNKTECHNIKPLUS # JOURNAL e3-4 ISSUE 7 - YEAR 2 




About 



8 We provide the author with the option to choose from 2 re- 
view processes: the traditional, anonymous, close one, as 
well as, a contemporary, onymous, open review in our pri- 
vate mailing list for Peer Discussion. 

9 Under the Clause O : We immediately accept for publication 
a research paper directly resulting from a Project Report, 
or a Diploma-, Master-, or PhD-thesis, which already the 
author has successfully defended before a committee of ex- 
perts, as long as he can mention 2 members of this commit- 
tee who approved his Work. 

10 Under the Clause 0 : We immediately accept for publication 
any paper which is not Openly Accessible on the Internet. 

11 We immediately publish online a paper, as soon as it is 
accepted for publication in the Journal. 

12 We quickly publish an extra issue — that is in excess of 
the 3 issues we publish a year — as soon as the review 
process of 3 papers is completed. 

Reviewers - Every peer may voluntarily become a reviewer 
of the Journal in his skillfulness for as long as he wishes. 
In addition, each author of the Journal must review one paper 
in his expertness for each one of his published papers. 

Readers - Every reader is a potential post - reviewer : we 

welcome comments and post -reviews in our private mailing list 
for Peer Discussion. 

Editors - Every editor owns a PhD degree — to objectively 
prove that he really has the working experience of passing 
through the dominant publishing system. An editor pre-reviews 
a paper in order to check its compliance to our guiding prin- 
ciples and to select the appropriate reviewers of it. We can 
accept for consideration papers only in the expertise areas 
currently shown in the Editorial Team page, above. However, 
since we are very willing to amplify and extend the Scope of 
the Journal, we welcome the volunteer expert, in any related 
subject, who wants to join the Editorial Team as long as he 
unreservedly accepts our guiding principles. 

Electronic Publishing 

We regularly use the Free Libre Open Source Software Libre 
Office with the Free Liberation Mono font and the Freewares 
PDFCreator and PDF-Xchange Viewer. We also use, with some ba- 
sic html code of ours: the Free Open Source Software Open 
Journal System OJS by the Public Knowledge Project PKP in- 
stalled in our website, and the Free Open Digital Library of 



SUNDAY 31 MAY 2015 



e3-5 



FUNKTECHNIKPLUS # JOURNAL 



About 



Internet Archive website, where we upload Issues, Paper re- 
prints, About documents, and Volumes, in both portrait and 
landscape orientations, for exceptionally clear online read- 
ing with the Free Open Source BookReader. 

Submissions 

We can consider only papers submitted in a format which is 
fully compatible with LibreOffice — preferably in odt format. 

Legal Notice - It is taken for granted that the submitter- 
correspondent author accepts, without any reservation, the 
totality of our publication conditions as they are analyti- 
cally detailed here, in this About, as well as, that he also 
carries, in the case of a paper by multiple authors, the in- 
dependent will of each one of his coauthors to unreservedly 
accept all the aforementioned conditions for their paper. 

Internet Addresses 

Internet Publishing Website : ftpj.otoiser.org 

Internet Archive Digital Library : archive . org/details/§f tpj 

Printing-on-Demand : pod§f tpj . otoiser . org 

Principal Contact : principal-contact§f tpj . otoiser . org 

Technical Support : technical-support§f tpj . otoiser . org 

Editorial Team-Technical Support List : etts.ftpj.otoiser.org 

Peer Discussion List : peers.ftpj.otoiser.org 

Submissions : sub§f tpj . otoiser . org 

Sample Paper Template : template.ftpj.otoiser.org 



ARG NfP Aol 

Antennas Research Group 
Not-for-Profit Association of Individuals * 

arg.op4.eu - arg@op4.eu 

HauptstraBe 52, 2831 Scheiblingkirchen, Austria 

* The Constitution of Greece, Article: 12(3) 2008: 

www . hellenicpar liament . gr/en/Vouli-ton-Ellinon/To-Politevma 

* The Hellenic Supreme Court of Civil and Penal Law: 
www.areiospagos.gr/en/ - Court Rulings : Civil |A1 | 511 | 2008 



This document is licensed under a Creative Commons Attribution 4.0 
International License - https : //creativecommons . org/licenses/by/4 . 0/ 



FUNKTECHNIKPLUS # JOURNAL 



e3—6 



ISSUE 7 - YEAR 2 



TELECOMMUNICATIONS ENGINEERING 



METROLOGIE 



Measurement Uncertainty in Network Analyzers: 
Differential Error Analysis of Error Models 
Part 3: Short One-Port Calibration -Comparison 

N.I. Yannopoulou, P.E. Zimourtopoulos * 

Antennas Research Group, Austria - Hellas [l, 2] 

EECE Dept, Democritus University of Thrace, Hellas [2] 

Abstract 



In order to demonstrate the usefulness of the only one 
existing method for systematic error estimation in VNA (Vec- 
tor Network Analyzer) measurements by using complex DERs 
(Differential Error Regions), we compare one-port VNA mea- 
surements after the two well-known calibration techniques: 
the quick reflection response, that uses only a single S 
(Short circuit) standard, and the time-consuming full one- 
port, that uses a triple of SLO standards (Short circuit, 
matching Load, Open circuit). For both calibration tech- 
niques, the comparison concerns: (a) a 3D geometric represen- 
tation of the difference between VNA readings and measure- 
ments, and (b) a number of presentation figures for the DERs 
and their polar DEls (Differential Error Intervals) of the 
reflection coefficient, as well as, the DERs and their rec- 
tangular DEIs of the corresponding input impedance. In this 
paper, we present the application of this method to an AUT 
(Antenna Under Test) selected to highlight the existence of 
practical cases in which the time consuming calibration tech- 
nique results a systematic error estimation stripe including 
almost all of that of quick calibration. 



Introduction 

The systematic error in a 
full one-port calibrated VNA 
measurement p of a given one- 
port DUT (Device Under Test) 
is already estimated by its 
DER [1] - [2] : 

p = (m - D)/[M(m - D) + R] (1) 



dp = [- RdD - (m - D) 2 dM - 
- (m - D)dR + Rdm] / 

/ [M(m - D) + R] 2 (2) 

where m is the VNA complex 
reading and D, M and R are 
the complex system errors of 
Fig. 1. 

The relations holding be- 
tween this complex reflection 



SUNDAY 15 DECEMBER 2013 



V2-41 



FUNKTECHNIKPLUS # JOURNAL 



N.I. YANNOPOULOU, P.E. ZIMOURTOPOULOS 



coefficient p and its respec- 
tive impedance Z, as well as, 
between their DERs are [1] - [2] : 

Z = Z 0 (l + p)/(l-p) (3) 

dZ = 2Z 0 dp/(l - p) 2 (4) 

In this paper, we express 
the DERs for systematic error 
estimation in VNA measure- 
ments calibrated by the much 
simpler and quicker reflec- 
tion response technique, in 
order to be in place to make 
some practical decisions from 
the different calibration tech- 
niques comparison. 



1 




R 



Fig. 1: Full one-port error 

model 

Response Calibration 

The reflection response ca- 
libration technique can be 
accomplished with the mea- 
surement of only one standard 
load, instead of three in 
full one-port, usually of a S 
short circuit [3] -[4]. This 
means that the flow graph of 
Fig. 1 is simplified a lot, 
since the two surrounded by 
dashed boxes system error 
branches of directivity D and 
source match M do not exist, 
equivalently D = 0 and M = 0 
and (1) results to: 



R = m/ps = s/S (5) 

where s is the VNA complex 
reading of the S short cir- 
cuit standard with a nominal 
value of S = - 1, m is the com- 
plex reading of a given DUT 
and ps is its complex reflec- 
tion coefficient as it is 
measured after this response 
calibration : 

ps = (m/s)S (6) 

which, from (2), has the dif- 
ferential error: 

dps = (S/s)dm - (Sm/s 2 )ds + 

+ (m/s)dS (7) 

The corresponding total DER 
is then the sum of L = 3 par- 
allelograms. Therefore, this 
DER contour is a polygonal 
line with 4L = 12 line seg- 
ments and vertices at most, 
in contrast with the DER of 
the measurement after a SLO 
full one-port calibration, 
which is a piecewise curve com- 
posed of 4(L - 1) = 24 line 
segments, 4(L - 1) = 24 circu- 
lar arcs and 8(L-l)=48 ver- 
tices, at most [1] - [2] . 

Application Results 

By following the error es- 
timation process, we already 
detailed in [i]-[2], we take 
as dS the considered manufac- 
turers' standard S uncer- 
tainty data: 

-0.01 < d | S | < 0, -2° < diS < +2° 



FUNKTECHNIKPLUS # JOURNAL 



V2-42 



ISSUE 2 - YEAR 1 



VNA UNCERTAINTY PART 3: SHORT ONE-PORT CALIBRATION - COMPARISON 



and as dm and ds the VNA in- 
accuracy of ±1 digit in LSD 
of their corresponding read- 
ings, for either the ampli- 
tude in decibels or the phase 
in degrees. Moreover, the one- 
port DUT that was considered 
is the same typical UHF ground- 
plane antenna (that is: AUT) 
mentioned in [1] . 

The difference between the 
3 nominal values (-1, 0, 1) 

of the 3 full one-port cali- 
bration standards (S, L, 0), 
respectively, and their 3 cor- 
responding VNA readings (s, 

1, o), can be estimated by 
the extent of the surfaces 
shown in the triptych of Fig. 

2, where the vertical axis 
segment represents the range 
of the distinct stepped fre- 
quencies. Each surface is for- 
med by parallel to horizontal 
plane lines. Each such line 
expresses the complex differ- 
ence between the standard no- 
minal value and its corre- 
sponding VNA reading, in each 
stepped frequency. 

In the triptych of Fig. 3, 
and from left to right we 
have the difference surfaces 
made by distance lines be- 
tween : 

(a) the measured reflection 
coefficient p after a full 
SLO one-port calibration 
(black solid points) and the 
corresponding VNA readings m 
for the AUT measurement (col- 
ored magenta points), 



(b) the measured reflection 
coefficient ps after S re- 
sponse calibration (black 
ring points) and the corre- 
sponding VNA readings m for 
the AUT measurement (colored 
magenta points), and 

(c) the two measurements (p, 
ps) . 

All the involved, previ- 
ously shown, quantities are 
projected on the horizontal 
complex plane of Fig. 4. The 
magenta colored spiral repre- 
sents m, while, the black 
curves the reflection coeffi- 
cient: solid points, for p, 

and ring points for ps. All 
of 1 VNA readings are close 
enough to complex origin (co- 
lored green points). It is 
rather difficult to distin- 
guish the two curves for s 
and o VNA readings, which are 
close enough to the unit cir- 
cle circumference (colored 
red solid points and colored 
blue ring point, respec- 
tively) . 

The p-DERs and ps-DERs, 
for all 4 MHz stepped fre- 
quencies covering the range 
of [600, 1000] MHz, are over- 
lapped on the complex plane 
of Fig. 5, forming a light 
and a dark gray stripes, re- 
spectively. From each stripe 
we selected 11 DERs out of 
101, drawn with dark gray and 
white colors respectively, to 
illustrate their outline de- 
pendence on frequency. 



SUNDAY 15 DECEMBER 2013 



V2-43 



FUNKTECHNIKPLUS # JOURNAL 



N.I. YANNOPOULOU, P.E. ZIM0URT0P0UL0S 




Fig. 2: Difference between s and S, 1 and L, o and 0 




Fig. 3: Difference between m and p, m and ps, p and ps. 



FUNKTECHNIKPLUS # JOURNAL 



V2-44 



ISSUE 2 - YEAR 1 



VNA UNCERTAINTY PART 3: SHORT ONE-PORT CALIBRATION - COMPARISON 




Fig. 4: VNA s, 1, o, m readings and p, ps measurements. 



Moreover, we selected to 
magnify a part of this figure 
in the sub-range of [892, 
1000] MHz, to further illus- 
trate the DER outlines and 
their overlapping in Fig. 6, 
where the clearly shown rip- 
ple of the simple response 
calibration stripe over the 
relatively smooth full one- 
port calibration stripe re- 
veals the superiority of the 
latter in the production of 
more accurate measurements. 

The comparison between the 
AUT measurements based on 



these two calibration tech- 
niques is extended to the 
comparison against the fre- 
quency : 

(a) of the computed polar 
DEIs of the reflection coef- 
ficient magnitude and argu- 
ment stripes in Fig. 7, 

(b) of the rectangular DEIs 
for the corresponding R input 
resistance and X input reac- 
tance stripes, in Fig. 8 and 

(c) of the Z-DERs, and Zs- 
DERs stripes in Fig. 9. 



V2-45 



SUNDAY 15 DECEMBER 2013 



FUNKTECHNIKPLUS # JOURNAL 



N.I. YANNOPOULOU, P.E. ZIMOURTOPOULOS 




-.45 



-.45 



f , Mhz 



600 



Fig. 5: Complex p-DERs and ps-DERs in [600, 1000] MHz 




Fig. 6: Complex p-DERs and ps-DERs in [892, 1000] MHz 



V2-46 



FUNKTECHNIKPLUS # JOURNAL 



ISSUE 2 - YEAR 1 



VNA UNCERTAINTY PART 3: SHORT ONE-PORT CALIBRATION - COMPARISON 




600 700 800 900 1000 



Frequency, MHz 

Fig. 7: Polar DEls of reflection coefficient 




600 700 800 900 1000 

Frequency, MHz 

Fig. 8: Rectangular DEIs of input impedance 



SUNDAY 15 DECEMBER 2013 V2-47 FUNKTECHNIKPLUS # JOURNAL 



N.I. YANNOPOULOU, P.E. ZIMOURTOPOULOS 




Fig. 9: Complex Z-DERs and Zs-DERs in [600, 1000] MHz 



Conclusion in selection of full one-port 

From all that, it must be calibration over the reflec- 
clear now that in this inten- tion response one, due to their 
tionally selected for presen- remarkable in all aspects co- 
tation particular AUT case incidence. Of course this is 
there was no advantage at all just another one conclusion 

a-posteriori . 



FUNKTECHNIKPLUS # JOURNAL 



V2-48 



ISSUE 2 - YEAR 1 





VNA UNCERTAINTY PART 3: SHORT ONE-PORT CALIBRATION - COMPARISON 

References * 

[1] Yannopoulou N., Zimourtopoulos P., "Total Differential 
Errors in One Port Network Analyzer Measurements with 
Application to Antenna Impedance", Radioengineering, 
Vol. 16, No. 2, June 2007, pp. 1-8 

"www . radioeng . cz/f ulltexts/2007/07_02_01_08 . pdf" 

[2] Yannopoulou N.I., Zimourtopoulos P.E., "Measurement Un- 
certainty in Network Analyzers: Differential Error Anal- 
ysis of Error Models Part 1: Full One-Port Calibration", 
FunkTechnikPlus # Journal, Issue 1, October 2013, pp. 
17-22 

"www. otoiser . org/index . php/f tpj/article/view/42" 

[3] HP, "Vector Measurements of High Frequency Networks", 
Hewlett-Packard, 1989, pp. 2-13, 2-15, 3-11, 3-12 

[4] AGILENT, "OPEN/SHORT Response Calibration (reflection 
test), Calibration Types and Characteristics" 

"http : //ena. support . keysight.com/e507lc/manuals/webhelp/en 
g/measurement/calibration/calibration . htm" 

*Active Links: 15.12.2013 - Inactive Links : FTP#J Link 

Updates: "http://updates.ftpj .otoiser.org/" 

Preprint Versions 

"Comparison of Error Estimation by DERs in One-Port S 
and SLO Calibrated VNA Measurements and Application" 

Nikolitsa Yannopoulou, Petros Zimourtopoulos 
"http : //arxiv . org/abs/1102 . 4239" 

Follow-Up Research Paper 

Not until now 

Previous Publication in FUNKTECHNIKPLUS # JOURNAL 

"Measurement Uncertainty in Network Analyzers: 
Differential Error Analysis of Error Models Part 2: 

Full Two-Port Calibration", Issue 1, pp. 23-30 

* About The Authors 

Nikolitsa Yannopoulou , Issue 1, p. 15 

Petros Zimourtopoulos , Issue 1, p. 15 



This paper is licensed under a Creative Commons Attribution 4.0 
International License - https : //creativecommons . or q/ licenses /by/ 4 . 0/ 



SUNDAY 15 DECEMBER 2013 



V2-49 



FUNKTECHNIKPLUS # JOURNAL 



[ This Page Intentionally Left Blank ] 



[ This Page Intentionally Left Blank ] 



[ This Page Intentionally Left Blank ] 




[ This Page Intentionally Left Blank ] 



In case of any doubt, 
download the genuine papers from 

genuine . f tpj . otoiser . org 



FRONT COVER VIGNETTE 

A faded synthesis of an anthemion rooted in a meandros 

The thirteen-leaf is a symbol for a life tree leaf. 

"Herakles and Kerberos", ca. 530-500 BC, 
by Paseas, the Kerberos Painter, 
Museum of Fine Arts, Boston. 

www. mf a. or g/collect ions/object /plate -153852 

The simple meandros is a symbol for eternal immortality. 

"Warrior with a phiale", ca. 480-460 BC, 

by Berliner Maler, 

Museo Archeologico Regionale "Antonio Salinas" di Palermo, 
commons .wikimedia. org/wiki/File: War rior_MAR_Palermo_Nl2l34.jpg